Diffractive trifocal lens

ABSTRACT

A diffractive multifocal lens is disclosed, comprising an optical element having at least one diffractive surface, the surface profile comprising a plurality of annular concentric zones. The optical thickness of the surface profile changes monotonically with radius within each zone, while a distinct step in optical thickness at the junction between adjacent zones defines a step height. The step heights for respective zones may differ from one zone to another periodically so as to tailor diffraction order efficiencies of the optical element, in one example of a trifocal lens, step heights alternate between two values, the even-numbered step heights being lower than the odd-numbered step heights. By plotting a topographical representation of the diffraction efficiencies resulting from such a surface profile, step heights may be optimized to direct a desired level of light power into the diffraction orders corresponding to near, intermediate, and distance vision, thereby optimizing the performance of the multifocal lens.

RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 16/933,106, filed Jul. 20, 2020, now U.S. Pat. No. 11,199,725,which is a continuation of U.S. patent application Ser. No. 16/250,866,filed Jan. 17, 2019, now U.S. Pat. No. 10,725,320, which is acontinuation of U.S. patent application Ser. No. 15/136,770, filed Apr.22, 2016, now U.S. Pat. No. 10,209,533, which is a continuation of U.S.patent application Ser. No. 13/201,440, filed Aug. 12, 2011, now U.S.Pat. No. 9,320,594, which is a 371 National Phase Application ofInternational Patent Application No. PCT/US2010/024165, filed Feb. 12,2010, which claims the benefit of U.S. Provisional Patent ApplicationNo. 61/207,409, filed Feb. 12, 2009, the disclosures of which are herebyincorporated by reference in their entirety.

TECHNICAL FIELD

The present invention relates generally to the field of diffractiveoptics and ophthamology, and more specifically, to the design andconstruction of corrective multifocal intraocular or contact lensesuseful for treating presbyopia.

BACKGROUND

Bifocal and trifocal contact lenses are commonly used to treatpresbyopia, a condition in which the eye exhibits a progressivelydiminished ability to focus on near objects. Human beings becomepresbyopic due to aging, and the effect typically becomes noticeablestarting at about the age of 40-45 years, when they discover they needreading glasses. Presbyopic individuals who wear corrective lenses maythen find that they need two separate prescriptions, preferably withinthe same bifocal lens, one for reading (near) and another for driving(distance). A trifocal lens further improves vision at intermediatedistances, for example, when working at a computer. An intraocular lens(IOL) is an artificial replacement lens that may be used as analternative to a contact lens or eyeglasses. An IOL is often implantedin place of the natural eye lens during cataract surgery. Anintracorneal lens (ICL) is an artificial lens that is implanted into thecornea.

Conventional corrective optics are typically refractive lenses, meaningthat they bend and focus light rays reflected from an object to form afocused image of the object on the retina. The bending of the light raysis dictated by Snell's law which describes the degree of bending thatoccurs as light rays cross the boundary of two materials with distinctindices of refraction.

Diffractive lenses have a repeating structure that may be formed in thesurface of an optical element by a fabrication method such as, forexample, cutting the surface using a lathe that may be equipped with acutting head made of a hard mineral such as diamond or sapphire; directwrite patterning using a high energy beam such as a laser beam orelectron beam or a similar method of ablating the surface; etching thesurface using a photolithographic patterning process; or molding thesurface. The diffractive structure is typically a series of concentricannular zones, which requires each zone to become progressively narrowerfrom the center to the edge of the lens. There may be, for example,20-30 zones between the center and the edge of the lens. The surfaceprofile within each zone is typically a smoothly varying function suchas an arc, a parabola, or a line. At the outer periphery of each zonethere is a discrete step in the vertical surface profile, the stepheight typically measuring about 0.5-3 microns. The resulting surfacestructure acts as a circularly symmetric diffraction grating thatdisperses light into multiple diffraction orders, each diffraction orderhaving a consecutive number, zero, one, two, and so forth.

“Diffraction efficiency” refers to the percentage of incident lightpower transmitted into each of the various diffractive orders comprisingthe diffraction pattern at the focal plane. If the zones have equalsurface areas and are radially symmetric, they focus light of differentdiffraction orders onto the optical axis of the lens, each diffractionorder having its own distinct foci. Thus, the diffractive lens acts as amultifocal lens having many discrete foci. For example, a diffractivebifocal lens simultaneously provides sharp retinal images of objects attwo different distances, as well as two corresponding out-of-focusimages. The human visual system has the ability to select from among thedifferent retinal images, thereby enabling simultaneous multifocalvision using a single diffractive lens.

Diffractive lenses may be used as contact lenses and IOLs for correctingpresbyopia. In such an application, the lens comprises one refractivesurface and one diffractive surface. In practice, the light energypassing through a diffractive lens is typically concentrated into one,two, or three diffractive orders, while contributing an insignificantamount of light energy to other diffractive orders. With respect todiffractive corrective lenses, for example, a high diffractionefficiency for the zeroth order connotes a greater improvement invisibility at far distances. The amount of optical energy directed intoeach diffraction order is dictated by the zonal step heights. A lensdesigner may choose, for the diffractive surface features of a bifocallens, step heights so as to introduce, for example, a one-halfwavelength phase change between adjacent zones, which directsapproximately 40% of the incident light into the zeroth diffractionorder corresponding to distance vision, and 40% into the positive firstdiffractive order, corresponding to near vision. The remaining 20% ofthe incident light in a conventional bifocal lens is directed to otherdiffraction orders that are not useful for vision.

Existing designs for multifocal intraocular and contact lenses useeither refractive optics, a combination refractive/diffractive design,or diffractive lenses that direct light into a single diffractive order.For example, U.S. Pat. No. 5,344,447 to Swanson, discloses a trifocalIOL design that enhances distance vision using a combination lens havinga refractive surface and a diffractive surface. Each diffractive zone inthis case corresponds to a binary step. This lens distributes lightapproximately equally between the positive first, zeroth, and negativefirst diffraction order. However, a drawback to this configuration isthat excess light is directed into other higher diffractive orders,reducing visual quality. Furthermore, this configuration makes the powerof the underlying carrier lens more difficult to predict becausedistance vision is dictated by a combination of the lens' refractivepower with the diffractive power of the minus one diffractive order.None of the existing alternatives succeeds in directing enough lightinto a diffractive order that corresponds to an intermediate focaldistance, and therefore trifocal contact lenses and IOLs fail to performequally well throughout the full focal range. For example, U.S. Pat. No.7,441,894, issued to Zhang, et al. discloses a trifocal intraocular lenshaving diffractive zones of varying areas capable of directing about25-28% of incident light into the near and far foci, but only about 10%of the incident light is directed into the intermediate focus.

SUMMARY

A diffractive multifocal lens is disclosed, comprising an opticalelement having at least one diffractive surface, the surface profile ofwhich comprises a plurality of concentric annular zones. The opticalthickness of the radial surface profile changes monotonically withineach zone. A distinct step in optical thickness occurs at the outerperiphery of each zone, the size of which is referred to as a “stepheight.” According to a preferred embodiment, instead of being equal,the step heights for adjacent zones differ from one zone to anotherperiodically so as to tailor diffraction order efficiencies of theoptical element. There is particular interest in increasing at least thefirst order diffraction efficiency of the optical element to addressintermediate distance vision for trifocal lenses.

In one example of a trifocal lens, the step heights alternate betweentwo values, the even-numbered step heights being lower than theodd-numbered step heights. In alternative embodiments, the even-numberedstep heights may be higher than the odd-numbered step heights, orsuccessive step heights may alternate between three or more values. Instill another embodiment, the pattern of step heights gradually changesfrom the center to the edge of the lens. According to one suchembodiment, the center of the lens is trifocal, but it becomesprogressively bifocal toward the edge of the lens. By modeling andplotting a topographical representation of the diffraction efficienciesresulting from such a surface profile, dimension parameters such as stepheight values may be selected so as to achieve directing a desiredproportion of light power into designated diffraction orders, therebyoptimizing the distance, intermediate, and near performance of themultifocal lens.

It is to be understood that this summary is provided as a means forgenerally determining what follows in the drawings and detaileddescription, and is not intended to limit the scope of the invention.Objects, features and advantages of the invention will be readilyunderstood upon consideration of the following detailed descriptiontaken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a commercially available prior art diffractive bifocalintraocular lens.

FIG. 2 is a magnified view of the surface of a central zone of the priorart diffractive bifocal intraocular lens shown in FIG. 1 , in which thecenter of the lens is located at the lower right hand corner of theimage.

FIG. 3 is a plot of the optical phase change introduced by aconventional prior art bifocal diffractive lens as a function of radiusacross five zones of the lens, showing generally equal step heights.

FIG. 4 is a cross-sectional view of the radial surface profile for adiffractive structure according to a preferred embodiment of a noveltrifocal diffractive lens, showing two alternating step heights.

FIG. 5 is a plot of the optical phase change introduced by thediffractive structure shown in FIG. 4 , as a function of radius, showingcorresponding alternating step heights for five representative zones.

FIG. 6 is a series of computer-generated two-dimensional topographicplots showing diffraction efficiencies that result from differentchoices of values for the alternating step heights in the optical phaseprofile of FIG. 5 .

FIG. 7 is a plot of the optical phase change introduced by a graduatedtrifocal/bifocal diffractive structure as a function of radius, showingcorresponding alternating step heights.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention will be readily understood by the followingdetailed description in conjunction with the accompanying drawings. Tofacilitate this description, like reference numerals designate likestructural elements. In the following description many details are setforth to provide an understanding of the disclosed embodiments of theinvention. However, upon reviewing this disclosure, it will becomeapparent to one skilled in the art that not all of the disclosed detailsmay be required to practice the claimed invention and that alternativeembodiments might be constructed without departing from the principlesof the invention.

Referring to FIG. 1 , an existing diffractive bifocal intraocular lens100 is shown. Lens 100 is commercially known as a ReSTOR® lens implant,and is available from Alcon Laboratories, Inc. of Fort Worth, Tex. Thelens implant comprises a pair of extensions 101 connected to a centraloptical element having at least one optical surface 102 in which adiffractive profile pattern is formed within radial zones. FIG. 2 showsa magnified view of optical surface 102, in which a generally radiallysymmetric surface profile pattern for a series of concentric annularzones 104 features, at the outer periphery of each zone, a discrete step106, having step height 108. The widths of zones 104 generally decreasefrom the center toward the edge of lens 100 so that a central zone width110 may be significantly wider than an edge zone width 112. Zones ofdifferent widths preferably represent equal surface areas. In general,if the step height 108 introduces a phase delay of 2π, a single powerlens results, i.e., the lens will have a single focus; if the stepheight 108 introduces a phase delay not equal to a multiple of 2π, abifocal lens results.

FIG. 3 shows a radial profile 120 of the optical phase changeexperienced by an incident light wave as it passes through thediffractive lens 100. Radial profile 120 may be achieved by diffractivestructures generally having sawtooth-shaped elements, or by varying theindex of refraction of the lens material. The radial dependence of thephase change Φ(r) is given byΦ(r)=2παp[j−r ²/(2pλ ₀ F ₀)]   (1)α=λ/λ₀[n(λ)−n′(λ)]/[n(λ₀)−n′(λ₀)], for radii r within the j ^(th)zone  (2)in which λ₀ is the design wavelength, i.e., the wavelength at which aphase change of 2π occurs at each zone boundary; n is the index ofrefraction of the lens material; F₀ is the focal length when theillumination wavelength λ=λ₀; n′ is the index of refraction of thematerial surrounding the lens; and p is an integer that represents themaximum phase modulation as a multiple of 2π. The cross-section of theactual optical surface, corresponding to the concentric regions 104shown in FIG. 2 is related to the radial phase change profile. Thecorresponding maximum height of the surface relief of optical surface102 is given byh _(max)(r)=pλ ₀[n(λ₀)−n′(λ₀)]  (3)and is typically about 5 microns.

Referring to FIG. 3 , elements of radial phase profile 120 have asawtooth shape 122, characterized by sharp peaks having a leading edge124 that rises from a first value 125 normalized to zero, gradually to apeak value 126, and a trailing edge 128 that falls abruptly from thepeak value 126 back to the initial height 125. The central ring width110 corresponds to the radius of the first peak, and the edge ring width112 corresponds to the distance between the fourth and fifth peaks inthis example, in which peak values 126 are associated with substantiallyequal step heights. The radial phase profile of FIG. 3 is produced by asurface profile, the elements of which have a similar shape as sawtooth122, and which have an associated optical thickness profile that alsohas a similar shape as sawtooth 122. Existing bifocal intraocular lenses100 in this configuration typically have diffraction efficiencies of 40%into each of the zeroth and first diffractive orders (far and neardistances, respectively), and substantially smaller diffractionefficiencies for higher diffractive orders. As a result, distance andnear vision are enhanced, but intermediate vision is limited.

FIG. 4 shows a cross-sectional view of a physical surface profile 130 ofa diffractive structure fabricated in an upper optical surface 102 of alens according to a preferred embodiment. A lower surface of the lens,134, is a refractive surface. The radial width of each diffractiveannular zone 104 decreases from the center of the lens to the edge ofthe lens to maintain equal areas of the diffractive zones. The stepheights between each zone alternate between two values, starting withthe larger step height 136 for the transition between the central zoneand the first annular zone. A smaller step height 138 characterizes thetransition between the first and second zones. This alternating stepheight pattern is repeated out to the edge of the lens.

FIG. 5 shows a plot of the radial profile 140 of the optical phasechange Φ(r) experienced by an incident light wave as it passes throughan enhanced diffractive trifocal lens having the surface profile shownin FIG. 4 . Elements of radial profile 140 have a sawtooth shape 141similar to sawtooth shape 122, in which each of the concentric zones islocated at the same radius, but the step heights are not allsubstantially equal. Instead, a first set of peaks 142, having largerstep heights 144, alternate with a second set of peaks 146 havingsmaller step heights 148. These features of the phase profile correspondto surface profile step heights 136 and 138, respectively. Byalternating the step heights incident light power may be directed to thediffractive orders corresponding to distance, intermediate, and nearvision. According to a preferred embodiment exemplified below,odd-numbered step heights are greater than even-numbered step heights,though in alternative embodiments, the reverse may be stipulated, whileapplying the same methodology for optimizing the design.

FIG. 6 shows nine computer-generated topographic plots A-I ofdiffraction efficiencies for light power directed into the zeroth,+first, and +second diffraction orders. These diffraction ordersrepresent distance vision 152, intermediate vision 154, and near vision156, respectively for a diffractive multifocal lens having a generalizedsawtooth-shaped phase profile consistent with both FIGS. 3 and 5 , forwhich odd-numbered step heights and even-numbered step heights may takeon different values.

An expression for calculating diffraction efficiencies for the phaseprofile of FIG. 5 is derived by generalizing a scheme disclosed in anarticle by Faklis and Morris (Dean Faklis and G. Michael Morris,“Spectral Properties of Multiorder Diffractive Lenses,” Applied Optics,Vol. 34, No. 14, May 10, 1995), of which sections 1 and 2 are herebyincorporated by reference. Faklis and Morris present diffractionefficiencies relevant to the phase profile of FIG. 3 by deriving anexpression for the diffraction efficiency of the m^(th) diffractedorder, η_(m), by expanding the amplitude transmission function of thediffractive lens as a Fourier series, and extracting the Fouriercoefficient, c_(m). The diffraction efficiency, ƒ_(m), is then given by|c_(m)|². For a phase profile having substantially equal step heights,Faklis and Morris show that the diffraction efficiency may be expressedasη_(m)=[sin[π(αp−m)]/π(αp−m)].  (4)

By generalizing this derivation, it may be shown that the diffractionefficiency for the m^(th) diffracted order for the phase profile of FIG.5 , having two dimension parameters (e.g., alternating step heights) A1and A2, is given by:η_(m)(m,p,α,A1,A2)=qrt{¼{sinc[π/2(m−2A1pα)]²+2(−1)^(m)cos[π(A1−A2)pα]sinc[π/2(m−2A2pα)]+sinc[π/2(m−2A2pα)]²}}.  (5)

A similar derivation may be performed for a lens design having three ormore different step heights, yielding a different expression analogousto (5) for the specific example disclosed herein.

Referring to FIG. 6 , a graph of η_(m) for m=0 is shown in plots A, D,and G; a graph of θ_(m) for m=+1 is shown in plots B, E, and H; and agraph of η_(m) for m=+2 is shown in plots C, F, and I. In each of thenine plots, horizontal axes 158 represent step heights of even numberedprofile peaks, normalized to 2π, and vertical axes 160 represent stepheights of odd numbered profile peaks, normalized to 2π. The nine plotsthus each provide a topographic “map” on which may be located points ofinterest marked with an “X” corresponding to examples of differentdiffractive lens designs, dictated by the choice of step heights A1 andA2. The maps thus indicate, by their relative shading at the point ofinterest, the amount of power directed into each focal region to yielddifferent proportions of distance, intermediate, and near vision. Forexample, step heights A1 and A2 may be chosen so as to enhance thediffraction efficiencies for all three foci equally, or they may bechosen so that the zeroth order diffraction efficiency is twice that ofthe +first and +second orders, which would yield better distance vision,at the expense of intermediate vision. The lightest shaded regions ineach plot correspond to 100% diffraction efficiency, and the darkestshaded regions in each plot correspond to 0% diffraction efficiency. (Asimilar set of plots may be generated for a lens design having three ormore different step heights, A1, A2, and A3, according to acorresponding expression derived in a similar fashion as (5) above.)

Topographic plots A, B, and C in FIG. 6 illustrate a limiting case inwhich both the odd and even phase step heights 126, represented byvariables A1 and A2, are set to zero, i.e., this case represents theabsence of a diffractive surface pattern, which is essentially arefractive lens. Plotting the point (0,0) on each of topographic plotsA, B, and C yields an “X” in the lower left corner of the topographicfield. In plot A, the X coincides with a bright spot, indicating thatabout 100% of the light is directed into the zeroth “diffraction order”(distance); in plots B and C, the X coincides with a dark regionindicating that substantially no light is directed into the first andsecond diffraction orders (intermediate and near), consistent with theabsence of a multifocal diffraction pattern in this example.

Topographic plots D, E, and F in FIG. 6 illustrate the limiting casecorresponding to a conventional bifocal diffractive lens, having theprofile shown in FIGS. 3 , in which both the odd and even step heights126, represented by variables A1 and A2, are equal to 0.5*2π. Plottingcoordinates (0.5, 0.5) yields an “X” near the center of each plot. Inplots D and F, the X coincides with a grey region, indicating thatsubstantially equal portions of light power are directed into the zerothand second diffraction orders corresponding to distance and near vision.In plot E, the X coincides with a dark region, indicating thatsubstantially 0% of the light power is directed to the first diffractiveorder, corresponding to intermediate vision.

Topographic plots G, H and I in FIG. 6 illustrate a preferred embodimentof a multistep diffractive lens shown in FIG. 5 . In this example, oddstep heights 136 are assigned a value 0.7*2π and even step heights 138are assigned a value 0.3*2π, to yield optimal results. The reason forassigning these values can be appreciated by plotting the point (0.3,0.7) on each of topographic plots G, H and I, which yields an “X” in theupper left quadrant of each plat. In each of the plots, the X coincideswith a light grey-shaded region, the greyscale value indicating that thelight power is directed equally into each of the zeroth, first, andsecond diffractive orders, so that distance, intermediate, and nearvision are all substantially equally enhanced.

A more complex design example, for which a gradually decreasing phaseprofile is shown in FIG. 7 , provides a trifocal portion in the centerof the lens, progressing to a bifocal lens at the edge of the lens.According to this embodiment, a pair of alternating step heightsdecrease monotonically from first prescribed values 166 and 168 at thecenter of the lens to second prescribed values 170 and 172 at the edgeof the lens. For example, step height values A1 and A2 may be chosen tobe 0.3λ and 0.7λ at the center of the lens, and 0.1λ and 0.45λ at theedge of the lens respectively. A trifocal lens fabricated according tosuch a design would provide enhanced distance, intermediate, and nearvision for a person having small pupils, and it would favor distance andintermediate vision for a person having large pupils, gradually reducingthe near vision for large pupils. Visually, this would allow a person inbright lighting conditions to drive, see a computer monitor, and read,while under dark conditions when there is no need to read, it wouldallow the person to drive and see a dashboard more clearly.

Although certain embodiments have been illustrated and described herein,it will be appreciated by those of ordinary skill in the art that a widevariety of alternative or equivalent embodiments or implementationscalculated to achieve the same purposes may be substituted for theembodiments illustrated and described without departing from the scopeof the present invention. Those with skill in the art will readilyappreciate that embodiments in accordance with the present invention maybe implemented in a very wide variety of ways. This application isintended to cover any adaptations or variations of the embodimentsdiscussed herein.

The terms and expressions which have been employed in the foregoingspecification are used therein as terms of description and not oflimitation, and there is no intention, in the use of such terms andexpressions, to exclude equivalents of the features shown and describedor portions thereof, it being recognized that the scope of the inventionis defined and limited only by the claims that follow.

The invention claimed is:
 1. A diffractive multifocal lens comprising anoptical element having a first diffractive optical surface having aradial surface profile having a diffractive structure comprising aplurality of concentric annular zones concentric with a central zone andassignable, from the outer edge of the central zone to the edge of thelens, as alternating odd and even numbered zones each having a projectedsurface area that is equal, wherein the optical thickness of the lenschanges monotonically within each zone, a distinct step in opticalthickness occurs at the junction between the zones, the height of thesteps differs between each adjacent zone, and a pattern of step heightdifferences between two or more adjacent zones repeats periodically fromthe center to the edge of the lens so as to tailor the proportions ofthe diffraction order efficiencies of at least a zeroth, positive first,and positive second, diffractive order of the radial surface profile ofthe optical element, wherein the lens has a radial phase profile, of theoptical phase change introduced by the diffractive structure, andelements of the radial phase profile within each of the concentricannular zones have a sawtooth shape, comprising a sharp peak having aleading edge that rises from a first value normalized to zero, graduallyto a peak value, and a trailing edge that falls abruptly from the peakvalue back to the first value.
 2. The lens of claim 1, wherein the stepheights of the even numbered zones are greater than the step heights ofthe odd numbered zones.
 3. The lens of claim 2, wherein the differencein step heights between two adjacent zones gradually changes from thecenter to the edge of the lens.
 4. The lens of claim 1, wherein the stepheights of the even numbered zones are less than the step heights of oddnumbered zones.
 5. The lens of claim 4, wherein the difference in stepheights between two adjacent zones gradually changes from the center tothe edge of the lens.
 6. The lens of claim 1, wherein the step heightsof at least three radially, successive zones differ from one another. 7.The lens of claim 6, wherein the three or more step heights changegradually from the center to the edge of the lens.
 8. The lens of claim1, wherein the step heights are chosen so that the diffractionefficiencies of at least the zeroth, positive first, and positive secondorders are substantially equal.
 9. The lens of claim 1, wherein theradial surface profile height of each zone forms an arc.
 10. The lens ofclaim 1, wherein the radial surface profile height of each zoneincreases substantially linearly.
 11. The lens of claim 1, furthercomprising a second optical surface that is a refractive optical surfaceseparated from the first optical surface.
 12. The lens of claim 1,wherein the difference in step heights between two adjacent zonesgradually changes from the center to the edge of the lens.
 13. The lensof claim 1, adapted to be worn as a contact lens.
 14. The lens of claim1, adapted to be surgically implanted as an intraocular lens.
 15. Thelens of claim 1, wherein the lens comprises an intracorneal implant. 16.The lens of claim 1, wherein the diffraction efficiency in at least thepositive first diffractive order is increased to enhance intermediatedistance vision.